## Flow through Packed and Fluidized Beds | Fluid Mechanics | Flow through Packed and Fluidized Beds

When a fluid which may be liquid or gas flows through equipment and pipes which are filled with packing materials or solid obstruction(particles in case of catalyst powder) and even in the case of solid transport by means of the fluid flowing system, we come across a lot of variation in calculations and design such type of equipment. Flow condition certainly varies when they are not packing the equipment and when structured packing or random packing have used the flow of fluid differ with respect to the type of packing used. So initially the concept of  “Flow of fluid through packed and fluidized bed” dealt with fluid mechanics and then due to its wide application in the study of fluidized bed reactors and packed bed separation towers it has been given a different subject during the course of design sophisticated equipment for the process industry.

Pressure drop is one of the important parameters, which handles most of the design concepts. Types of equipment are modified according to the pressure drop calculations and a lot of equation like the Ergun equation is mostly used to do the job. Friction factor calculation and Friction loss determine the energy required to operate the equipment with full efficiency.

The latest reactor design is made with the view that it can be used to handle fluidized catalysts so that the catalyst can be regenerated and maintenance costs can be decreased and even it can to multi-task for producing products based on the demand. With the change in catalyst different products are obtained from the same raw materials in the same reactor. The replacement of the catalyst becomes easy and can be done with less cost, due to fluidization operation design.

Fluid Mechanics:
The fluid is defined as a substance which deforms continuously when subjected to shear stress. When an external force is applied it responds to these forces, it is a substance capable of flowing.

The analysis of fluid behaviour is based on fundamental laws of mechanics:

Conservation of mass, momentum, energy and laws of thermodynamics.

### Classification of fluid flows:

β’ Rheological consideration
β’ Dilational tensor
β’ Temporal variations
β’ Spatial dimensions
β’ Motions characteristics
β’ Fluid types
The fluid is gas or liquid and they are identified by the difference in their properties which can be understood as:
1. Gases Vs liquids:
based on the molecular behaviour
2. Continuum Vs discrete fluids:
continuum β individual molecular properties are negligible. Discrete fluid- each molecule treated separately
3. Perfect Vs real fluids:
real fluids β does not slip past a solid wall
4. Newton Vs non-Newtonian fluids:
Newton ΞΌ constant for fixed fluid temperature and pressure E.g. water. Non-Newtonian β ΞΌ varies E.g. milk.
5. Compressible Vs incompressible fluids:
Compressible fluids β density changes with applied pressures.
Incompressible fluids – density not changed by external forces acting.
Steady fluid flow β properties independent of time
Unsteady fluid flow β properties dependent on time

How to solve the problems in fluid flow systems?
A systematic procedure helps to solve the problems in the fluid flow systems, most of the confusion state can be avoided with a few steps. Analysis and investigation methods are the key background of the solving process.
Any of the condition statements can be resolved by investigations which are of two types:
1. Theoretical investigation
2. Experimental investigation.

A theoretical investigation is based on the numerical methodology whereas the experimental investigation is based on the experiments conducted in the laboratory which has the limitation of the scale-up. Analytical solutions are used in the theoretical investigation.
The physical analysis is based on either the force concept or the energy concept. It requires practical experience for the identification and classification of the parameters of the systems; all physical variables are a collection of information regarding the system.
Mathematical analysis is based on the forces concept, energy, or dimensional analysis. All the physical analysis information becomes the raw data for the mathematical analysis.

A static condition is in which the fluid is at rest where shear stress is negligible. There will be no shearing force as in the case of solid mechanics the same rules of statics are applicable to the static fluid.

The forces and stress present in the static fluid are
1. body forces β action through a distance e.g. gravity force, electromagnetic force
2. surface force β the virtue of direct contact
3. shear stress
4. stress tensor

Force between fluid and boundary acts at right angles to the boundary. The following are some of the important points to be remembered:

• Fluids flowing in pipes exhibit a velocity profile. In the laminar flow of Newtonian fluids, the velocity distribution with respect to the radius is Parabola with the apex at the centre line of the pipe
• Bernoulli equation applies to a non-viscous and incompressible fluid which does not exchange shaft work with the surroundings.
• The flow of gas along a pipe in the direction of decreasing pressure causes an increase in its specific volume.
• The maximum fluid velocity obtainable in a pipe of the constant cross-sectional area is the speed of sound.
• For a circular pipe completely filled with a liquid, the hydraulic radius is equal to the diameter of the pipe divided by four.
• A nozzle is a device that causes the interchange of internal and kinetic energies of a fluid as a result of changing cross-sectional area available for flow.
• For subsonic flow in a converging nozzle, the velocity increases and pressure decreases as the cross-section diminishes.
• In laminar flow, momentum is transferred as a result of the velocity gradient.
• The expansion of a gas in a nozzle to produce a high-velocity stream is a process that converts internal energy to kinetic energy.
• The turbine converts the internal energy of a high-pressure stream into shaft work.
• A throttling process does not change the temperature of ideal gases
• For an ideal fluid flow, the Reynolds number is infinite
• For pseudoplastic fluids increase in shear rate decreases the apparent viscosity
• A practical attains its terminal setting velocity when the sum of the buoyancy and drag forces is equal to the gravity force.
• The velocity of discharge of a liquid from a small orifice in the bottom of a wall of the vessel with a constant level head of liquid above the centre of the orifice in the vessel is proportional to βH
• For a fluidized bed, with the increase in expansion of the bed up to solids carryover from the bed the pressure drop across the bed remains constant
• A fluid A of specific gravity 1.0 and viscosity 0.001 N.s/m2 flows through a horizontal pipe of the circular cross-section. The fluid B of specific gravity 2 and viscosity 0.002 N.s/m2 flows through an identical pipe with the same average velocity as fluid A. The ratio of the pressure drop per unit length of pipe for fluid B to the pressure drop per unit length of pipe for fluid A is 2

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